Published: February 09, 2011

r 2011 American Chemical Society 3327 dx.doi.org/10.1021/jp1119876 | J. Phys. Chem. C 2011, 115, 3327–3331

ARTICLE

pubs.acs.org/JPCC

Electric Field and Size Effects on Atomic Structures andConduction Properties of Ultrathin Cu NanowiresCheng He,†,* Wenxue Zhang,‡ and Juanli Deng‡,§

†State Key Laboratory for Mechanical Behavior of Materials, School of Materials Science and Engineering, Xi’an Jiaotong University,Xi’an 710049, China‡School of Materials Science and Engineering, Chang’an University, Xi’an 710064, China§School of Natural and Applied Sciences, Northwestern Polytechnical University, Xi’an 710072, China

ABSTRACT: The ballistic transport properties of Cu nanowires (NWs) with diameter of0.2-1.0 nm under electric field (V = 1 V/Å) are reported for future applications asinterconnections in microelectronics. Our density-functional calculations show that, underV = 1 V/Å, with the wire diameter increasing, the number of conduction channels of a helicalatomic strand increases, whereas the number of a nonhelical atomic strand is constant withinthe considered size range. The structure, electronic, and charge properties of these two typesof Cu NWs exhibit distinctly different behaviors.

1. INTRODUCTION

There is increasing interest in developing metal nanowires(NWs) for possible applications for molecular electronicdevices.1 Cu as an interconnection in microelectronics is themost useful metal and the electronic transport of nanosizedinterconnections is one of the important characteristics for futuremicroelectronic applications.2,3 After the realization of the fab-rication metallic NWs, physical properties of metallic NWs aremeasured and calculated, especially their electron transportproperties. As the length and width scales of NWs are reducedto the mean free path of electrons, the electron transportmechanism changes from diffusive to ballistic. Now the electricconductance is independent of the length of the NWs and thequantum conduction G has been observed4 as expected from theLandauer formula.5 G is quantized in units of G0 = 2e

2/h where edenotes the electronic amount and h the Planck constant.Valence charge polarization by the locally entrapped coreelectron could be a possible mechanism for the ballistic trans-portation in the NW.6-8 The quantum conductance of metallicnanowires is an exciting emerging field of both fundamental andapplied relevance9-11 because metallic nanowires are buildingblocks for nanoelectronics12,13 and nanoelectromechanical sys-tems (NEMS).14 In the past decades, ultrathin metal nanowiresproduced by the tip retracting from nanoindentation in scanningtunnelling microscopy (STM), or by a mechanically controllablebreak junction (MCBJ), have been subjects of numerous experi-mental and theoretical studies.9,12,15 Both atomic structures andsize of NWs affect the transport properties.5,16-18 It is found thatG of the pentagonal Cu NWs with a [110] orientated structure isabout 4.5G0 without electric fields.4 When NW is sufficientlythin, beside the conventional structure,19 it can turn exotic.20

However, the effect of electric field strength V onGwith different

sizes, which is the precondition of the electronic transport, hasnot been considered systemically up to now.

In this contribution, the structures and conduction propertiesof ultrathin Cu NWs are determined by first-principles DFTcalculations. The atomic structures with diameter from 0.2-1.0 nm have been optimized. The density of states (DOS), G(V)function and the electronic distribution are also performed todetermine changes of atomic and electronic structures of CuNWs under electric fields.

2. COMPUTATIONAL DETAILS

The simulation is calculated by first-principles DFT, which isprovided byDMOL3 code.21,22 The generalized gradient approx-imation is employed to optimize geometrical structures andcalculate properties of Cu NWs with the Perdew-Burke-Ernzerhof correlation gradient correction.23,24 The all-electronrelativistic Kohn-Shamwave functions are expanded in the localatomic orbital basis set. The atomic orbitals are represented bythe double numerical basis including a d-polarization functionbasis set. The CuNWs are modeled in a tetragonal supercell with1D periodical boundary conditions along the NWs. Our outlinesof the used structures are directly referred to the results of Wanget al.25 The length of Cu NWs (L), which is determined by thedistance of the projection of mean locations of atom centers inthe first and 10th layers on the axis of the NWs, are chosen to be1.64 and 2.04 nm. It is because the distance between twoneighbor layers with a core atom in the NW is about (2)1/2/2times the distance without a core atom inNW. If L is shorter than

Received: December 17, 2010Revised: January 12, 2011

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6 layers, the helicity is hard to represent. If L is too long, it is toocostly in computational quantity and cannot improve the resultsfor the periodical boundary conditions. Hence, we choose 10layers. The k-point is set to 5 � 5 � 1 for all slabs, whichbrings out the convergence tolerance of energy of 2.0� 10-5 Ha(1 Ha = 27.2114 eV), maximum force of 0.004 Ha/Å, andmaximum displacement of 0.005 Å. V is directly applied alongthe axis of Cu NW in the DMOL3 program with values of 0 and1 V/Å. G(V) values are determined by the Landauer formula.26

The layer electronic distributions are carried out by the Mullikencharge analysis,27,28 which is performed using a projection of aLinear Combination of Atomic Orbitals (LCAO) basis and tospecify quantities such as atomic charge, bond population, chargetransfer, and so forth. LCAO supplies better information regard-ing the localization of the electrons in different atomic layers thana plane wave basis set does. The obtained charge e, but not theabsolute magnitude, displays a high degree of sensitivity to theatomic basis set and a relative distribution of charge with which ewas determined.29,30

3. RESULTS AND DISCUSSION

Figure 1 shows seven representative structures of Cu NWsobtained in the calculations. To characterize the structures ofCu nanowire, one can introduce the notation n1-n2-n3-n431

(n1 > n2 > n3 > n4, from outer to inner) to describe a multishellnanowire consisting of coaxial tubes with n1, n2, n3, n4 atomicrows on each shell where n shows the atomic number of oneatomic layer in the surface cell. Division as category, there are twodifferent structures of Cu NWs where a represents a nonhelicalstrand and b is a helical one. Thus, the structures in part A ofFigure 1 is defined as 3a, 3b, 4a, 4b and part B of Figure 1 is 6-1a,6-1b, and 12-6-1, where 12 shows the atomic number of oneatomic layer in the surface cell, 6 is in second-surface cell, and 1represents that in the core.25 Note that there could be fourpossible Cu nanowires (including noncompact nonhelical, com-pact nonhelical, left helical, and right helical) for 6-1 accordingto the results of a genetic algorithm (GA) global search.25 Thereis no difference inG(V) functions found in our simulation. Thus,the helical direction in 6-1b is neglected in our simulation.Among these four structures, the noncompact nonhelical nano-wire has higher energy than the compact nonhelical wire, and thehelical nanowire has the lowest energy, so we choose thenoncompact nonhelical as a and right helical as b and neglectthe middle energy structure. At the same time, the noncompactstructures of metal nanowires have been studied by Makita et al.and Gulseren et al.20 In general, the stable structures of Cu NWsare multishell packing composed of coaxial cylindrical shells ortubes. Each shell is formed by atom rows winding up helicallyside-by-side with different pitches of the helices, which have beentheoretically predicted for Al and Pb NWs32-34 and experimen-tally observed in Au NWs.35

L(V) functions of seven structures are determined fromFigure 1 and shown in Table 1. V, being similar to a stress field,deforms the atomic structures with atomic movements. Becausethe structures of 6-1a, 6-1b, 12-6-1 have the central axisatom and others do not have the central axis atom, the value ofL(V = 0) is different. When V = 0, the distance between twoneighboring layers at central axis (D) � 0.24 nm for 3a, 3b, 4b,whereas D � 0.18 nm for 6-1a, 6-1b, 12-6-1 in every layer.

For nonhelical NWs, L(V = 1 V/Å) is a little longer thanL(V = 0) for 3a, 4a, and L(V = 1 V/Å) is equal to L(V = 0) for 6-1a, where the atomic structure varies and D in the middle ofnonhelical NWs increases. The corresponding results of D areshown in Table 2. For example, for 3a, D4-5 = 0.22 nm, D5-6 =0.38 nm, and thusD4-6 = 0.60 nm. For 4a,D4-5 = 0.21 nm,D5-6

= 0.37 nm, and thus D4-6 = 0.58 nm, where the subscriptnumbers denote the corresponding layer numbers. As D4-6

increases, because of the nature of ballistic transport, the prob-ability of an electron jump between the two layers decreases andthus G decreases. The atoms in the odd layer move toward thedirections of both tips of the structure. Thus,D4-6(V = 1 V/Å) isabout 1.25 times of that for 3a, 4a, and 1.6 times for 6-1a atV = 0. Moreover, we find that the value of D4-6(V = 1 V/Å) isabout 0.59 nm for these three nonhelical NWs, which is onlydependent on V but independent of the nanowire diameter (d).The larger value of D5-6 is induced by the atomic movement ofthe atom in the seventh layer putting into the sixth layer.

Unlike nonhelical NWs, L(V = 1 V/Å) of helical NWs isshorter than L(V = 0). The reason is thatD(V = 1 V/Å) values oftwo tips decrease more strongly, which is shown in Table 2. Forinstance, compared V = 1 V/Å with V = 0, L drops from 2.16 to2.04 nm sinceD1-2 = 0.13 nm andD9-10 =0.14 nm for 3b, wherethe atoms in the odd layers go to the interstice of the next layerand the structure tends to continuously converge. Similar tononhelical NWs, atoms also accumulate on the both tips of NWs,whereas the atomic number in the middle part of NWs decreases.

Figure 1. Morphologies of Cu NWs as a function of V. V in V/Å. Thearrow shows the direction ofV. 3a, 3b, 4a, 4b are shown in (A) and 6-1a,6-1b, 12-6-1 are shown in (B).

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As L decreases, the rates of ballistic transport of even layersshould be increased.

According to the Landauer formula, the number of bandscrossing Fermi level Ef attributes to the number of conductionalchannels or the size of quantum conductance G.9 The sodetermined G(V = 0) and G(V = 1 V/Å) values of seven struc-tures with all conductional channels are shown in parts a-d ofFigures 2 and Table 1. For NWs with the same size, the atomicconfiguration of different isomers plays a significant role in deter-mining the details of energy bands at the vicinity of Fermi leveland thus the number of conduction bands crossing the Fermilevel. Namely,G(V) sensitively depends on the atomic structuresof the wires. For instance, 3b has two ballistic conduction channels,whereas 3a has three channels. When d is constant, G(V) of helicalNWs increases whileG(V) of nonhelical NWs decreases. Moreover,when V = 1 V/Å, G(d) of helical NWs increases and G(d) ofnonhelical is equal to 2 constantly. Table 1 shows the quantumconductance versus nanowire diameter atV = 0 andV = 1 V/Å. Onecan see that G (in unit of G0) approximately fit into a quadraticfunction of d (in unit of Å) at V = 0 as:25

GðV ¼ 0Þ ¼ 2:0þ 0:12� d2 ð1ÞThis is understandable because d2 gives the area of the cross sectionof theNWs, and, atV=1V/Å,G could be also proximatelyfitted intothe following quadratic function of wire d as:

GðV ¼ 1V=ÅÞ ¼ 2:0þ 11� d for helical NWs ð2Þ

GðV ¼ 1V=ÅÞ ¼ 2:0 for nonhelical NWs ð3Þ

This means that the electric field effect of helical NWs on G isno longer decided by the area of the cross section but decidedby the diameter. This is reasonable because the electric field isonly in the axis direction, and the structure has been changedalong the axis. Meanwhile, according to the results above,G(V = 1 V/Å) = 2.0 for 3a, 4a, 6-1a, which is independent ofthe size for nonhelical NWs. Because nonhelical NWs cannotremain stable when d > 9 Å in the simulation at present,12 weconsider G(V = 1 V/Å)� 2.0 for nonhelical NWs. It also provesthat the smallest value of G at V = 1 V/Å should be existed. Inother words, V = 1 V/Å is unable to make the nonhelical NWscollapse.

DOS of the seven structures observed by DFT are present inFigure 2. For instance, the largest peak of DOS below Ef is locatedbetween -1.79 and -0.41 eV under V = 0, whereas -1.76 and-0.23 eV under V = 1 for 4a. The case is similar for otherstructures. The position of largest peak obviously shifts right as Vincreases, which implies the energy of all structures increase. Thesize of DOS at Ef under V = 1 is 0.45 times of that under V = 0 for6-1a, whereas the comparison is 1.25 times that for 6-1b.These results for DOS ratios at Ef confirm the calculated resultsfrom Landauer formula shown in parts c and d of Figure 2.According to the figures, the size of DOS at Ef under V = 1 is 0.5times of that V = 1 is 0.5 times of that under V = 0 for 6-1a,whereas the comparison is 1.5 times for 6-1b. Although thepresent experimentation and simulation cannot realize V > 1V/Å, we predict that if V further increases without ruptures, themain peak of DOS can cross Ef, and G could be largely increased

Table 1. Diameter (d), Length (L), and Quantum Conduc-tion (G) Function of CuNWsObtained by DFTCalculationsa

wire d1 d2 d3 L1 L3 G1 G2 G3

3a 0.242 0.238 0.321 2.16 2.18 3 3 2

3b 0.212 0.214 0.232 2.16 2.04 2 2 3

4a 0.277 0.274 0.404 2.16 2.20 4 4 2

4b 0.288 0.286 0.312 2.16 2.08 3 3 5

6-1a 0.490 0.486 0.625 1.64 1.64 4 4 2

6-1b 0.418 0.424 0.433 1.64 1.54 4 4 6

12-6-1 0.942 0.936 0.956 1.64 1.61 11 10 13aUnits: d in nm, L in nm,G inG0,V in V/Å; the subscript 1 and 3 denotediameters obtained from our simulation without electrical field, andunder V = 1 V/Å, respectively. The subscript 2 denotes diametersobtained from ref 12 without electrical field.

Table 2. Distance between Two Neighboring Layers atCentral Axis (D) in the Calculations under V = 1 V/Å. a

wire D1-2 D2-3 D3-4 D4-5 D5-6 D6-7 D7-8 D8-9 D9-10

3a 0.17 0.20 0.24 0.22 0.38 0.22 0.26 0.26 0.23

3b 0.13 0.28 0.26 0.24 0.26 0.24 0.24 0.25 0.14

4a 0.22 0.25 0.22 0.21 0.37 0.24 0.25 0.22 0.22

4b 0.14 0.27 0.26 0.24 0.26 0.22 0.22 0.28 0.19

6-1a 0.08 0.22 0.17 0.20 0.38 0.09 0.15 0.25 0.10

6-1b 0.10 0.13 0.13 0.16 0.22 0.24 0.21 0.20 0.15

12-6-1 0.11 0.15 0.16 0.17 0.24 0.26 0.20 0.23 0.12aWhenV = 0, the distance between two neighboring layers at central axis(D)� 0.24 nm for 3a, 3b, 4b, whileD� 0.18 nm for 6-1a, 6-1b, 12-6-1 inevery layers. Figure 2. G(V), DOS of nonhelical NWs of 3a, 4a, 6-1a and helical

NWs of 3b, 4b, 6-1b, 12-6-1. Ef = 0 (vertical dotted line) is taken.

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Figure 3. Mulliken charge population of seven structures. The charges show the sum of each layer and the layer number is defined in Figure 1.

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for helical NWs. However, for nonhelical NWs, this peak dropsand would disappear as V further increases, where the ruptureoccurs and G = 0.

Mulliken charge e(V) functions of all structures are shown inFigure 3. The layer number is indexed in Figure 1. Under V = 0,e(V) functions of the both nonhelical and helical NWs are similarand homogeneous along the axes of the NWs. In nonhelicalNWs, the atoms in the center row are positively charged andothers are in reverse. Namely, the charge is enriched on thesurface due to the surface effect. WhenV = 1 V/Å,more electronslocalize at 5-8th layers of the polarized nonhelical NWs. Thus,the charges are negative in themiddle but positive in the both tipsdue to the movement of electrons. The minimum of e =-0.6 for3a, e =-0.7 for 4a, e =-1.4 for 6-1a is located at the sixth layer.The largest D value is also emerged at the sixth layer of thesestructures, which resists the electronic course. So, the electronaccumulation occurs only in the fifth and sixth layers, whereaselectrons in other layers are positive. This accumulation isunfavorable for the electronic transport.

However, in the case of helical NWs, electrons are homo-geneous distributed in all layers underV. The odd and even layerscombine and form a new layer, which increases the channelnumbers of ballistic transport. In addition, the absolute value of eunderV = 1 is larger than that underV = 0 due to smallerD valuesand the combination of layers.

4. CONCLUSIONS

In summary, we have studied the effect of electric fields onatomic and electronic structures and transport properties of CuNWs with diameter from 0.2-1.0 nm. The conduction of CuNWs generally increases with d at V = 0. When V = 1 V/Å, G(V)of helical NWs increases as size increases and a linear relationshipbetween G(V) and d is proposed, whereas that of a nonhelicalNWs is constant within the considered size range. A homoge-neous distribution of electrons along the axes of NWs benefitsthe ballistic electronic transport, whereas an inhomogeneous onedeteriorates the transport.

’AUTHOR INFORMATION

Corresponding Author*E-mail: hecheng@mail.xjtu.edu.cn. Tel: þ86 29 82668614.

’ACKNOWLEDGMENT

We acknowledge support from the National Key Basic Re-search and Development Program (Grant No. 2010CB631001).The authors also like to thank Professor Qing Jiang for fruitfuldiscussions. The authors acknowledge the computer resourcesprovided by Department of Materials Science and Engineering,Jilin University.

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